Topological Data Processing for Distributed Sensor Networks with Morse-Smale Decomposition

We are interested in topological analysis and processing of the large-scale distributed data generated by sensor networks. Naturally, a large-scale sensor network is deployed in a geometric region with possibly holes and complex shape, and is used to sample some smooth physical signal field. We are interested in both the topology of the discrete sensor field in terms of the sensing holes (voids without sufficient sensors deployed), as well as the topology of the signal field in terms of its critical points (local maxima, minima and saddles). Towards this end, we develop distributed algorithms to construct the Morse-Smale decomposition, and study the performance benefits obtained by this approach. The sensor field is decomposed into simply-connected pieces, inside each of which the sensor signal is homogeneous, i.e., the data flows uniformly from a local maximum to a local minimum. The Morse-Smale decomposition can be efficiently constructed in the network locally, after which applications such as iso-contour queries, data-guided navigation and routing, data aggregation, and topologically faithful signal reconstructions benefit tremendously from it.